Determine the profit table and draw the profit diagram for each of the following portfolios. For what range of values is the portfolio profitable and what is the maximum loss or profit? Assume that all options have a maturity of one year.

a. Long one European put option with strike price K=$90 which costs $6.

b. Long one European call option with strike price K=$100 which costs $4.

c. Long one share and short two European call options with strike price K=$100. The current price of the stock is $95 and the price of one call option is $4.

d. A strangle created from the options in (a) and (b). Superimpose the graph of the strangle on the graphs of the options.

e. When is the strangle in (d) profitable? What is the maximum loss or profit? Why and when would you use this strategy?